In the early 1950’s, Bohm simplified the 1935 EPR state from continuous coordinate-momentum space to discrete spin space by introducing a singlet state of two spin 1/2 particles. A more practical example of the EPR-Bohm state concerns the polarization states of photon pairs, such as the spin-zero state of a high energy photon pair disintegrated from the annihilation of positronium. Is it possible to have a realistic theory which provides correct predictions of the behavior of a particle similar to quantum theory and, at the same time, respects the description of physical reality by EPR as “complete”? Bohm and his followers have attempted a “hidden variable theory” to formulate the physical reality into the wavefunction of a particle or a pair of particles. The experimental testing of Bell’s inequality started from the early 1970’s. Most of the historical experiments concluded the violation of the Bell’s inequalities and thus disproved the local hidden variable theory.
In the early 1950’s, Bohm simplified the 1935 EPR state from continuous coordinate-momentum space to discrete spin space by introducing a singlet state of two spin 1/2 particles. A more practical example of the EPR-Bohm state concerns the polarization states of photon pairs, such as the spin-zero state of a high energy photon pair disintegrated from the annihilation of positronium. Is it possible to have a realistic theory which provides correct predictions of the behavior of a particle similar to quantum theory and, at the same time, respects the description of physical reality by EPR as “complete”? Bohm and his followers have attempted a “hidden variable theory” to formulate the physical reality into the wavefunction of a particle or a pair of particles. The experimental testing of Bell’s inequality started from the early 1970’s. Most of the historical experiments concluded the violation of the Bell’s inequalities and thus disproved the local hidden variable theory.
In 1935, Einstein, Podolsky, and Rosen (EPR) argued that (then new) quantum mechanics was incomplete. At the heart of EPR’s paradox was the strange non-local nature of an entangled state which allowed EPR to simultaneously assign local values for position and momentum of a particle. In 1964, John Bell proposed an inequality (Bell’s inequality) that must be satisfied by any local realistic theory. The experimental confirmation of quantum physics, i.e., the experimental test of Bell’s inequality, required a pair of particles in an entangled state. The experiments first performed in the early 1970s, followed by a series of experiments until now, have confirmed the violation of Bell’s inequality, strongly implying that local realistic descriptions of nature are not consistent with experimental observations. The early simplistic view of entanglement has now been significantly expanded to include mixed states and multiple particles. Moreover, theoretical and experimental studies on the nature of entanglement have led to quantum information science where entanglement is an essential resource. In this article, we briefly review the early experiments on Bell’s inequality and experimental attempts to close “loopholes” as well as some key experiments on quantum information.
An overview of the history of Bell’s inequality is given, beginning with the so-called EPR paradox originally put forward by Einstein, Podolsky and Rosen and the impossibility proof of von Neumann. Bell’s inequality, which ultimately shifted the discussion from arguments based on philosophically introduced postulates to the domain of experimental physics, is presented together with experimental attempts from the early 1970s to 2010s to violate this inequality. We introduce three historical loopholes in the experimental schemes which have prevented experimentalists from being able to fully disprove the possibility of a hidden-variables description of nature. Recent experimental data indicate that all the main loopholes are now closed for photons (albeit not simultaneously in one experiment). Besides the class of stochastic local realism that have been tested experimentally, some other possible classical interpretations are mentioned.
Abstract Chapter 14 examines entangled quantum systems, hidden variable theories and Bell’s inequality. In 1935, Einstein and collaborators, postulating the existence of elements of reality, analyzed an entangled system and concluded that quantum theory was incomplete. Their analysis is described using spin singlets, which are entangled states of two spin ½ particles. A possible avoidance of their conclusion is by using hidden variable theories. In analyzing a class of local hidden variable theories, John Bell derived an equality that could test them. This was done by experiments using entangled photons; their results violated the inequality, thereby establishing that quantum mechanics, not local hidden variable theories, is the correct description. Later theoretical analysis, and relevant experimental results, strongly supported this. A further theoretical analysis, involving just a single measurement, led to a pronounced conclusion: farewell to the elements of reality. Ditto as well to the spooky-action-at-a-distance problem that had so bothered Einstein.
The EPR paradox is shown to be a result of the wrong definitions in quantum mechanics of such physical quantities as momentum and position. The corrected definitions show that momentum and position of particles can be precisely defined simultaneously and uncertainty relations do not prevent it. Therefore, with correct definition of physical quantities in quantum mechanics, the paradox disappears. The Bohm Aharonov version of the EPR paradox is illustrated by the example of measuring the polarization of photon pairs. The common view of the two photon state radiated by a source is presented. The common Bell’s inequality is discussed and the simplest version of it for a specific hidden variable is derived. A possibility of an experimental study of whether a photon and its polarization are preexistent before measurements is considered.
Recent experiments on the classic Einstein-Podolsky-Rosen (EPR) setting claim to test the compatibility between nonlocal quantum entanglement and the (special) theory of relativity. Confirmation of quantum theory has led to the interpretation that Einstein's image of physical reality for each photon in the EPR pair cannot be maintained. A detailed critique on two representative experiments is presented following the original EPR notion of local realism. It is argued that relativity does not enter into the picture, however for the Bell-Bohm version of local realism in terms of hidden variables such experiments are significant. Of the two alternatives, namely incompleteness of quantum theory for describing an individual quantum system, and the ensemble view, it is only the former that has been ruled out by the experiments. An alternative approach gives a statistical ensemble interpretation of the observed data, and the significant conclusion that these experiments do not deny physical reality of the photon is obtained. After discussing the need for a photon model, a vortex structure is proposed based on the space-time invariant property-spin, and pure gauge fields. To test the prime role of spin for photons and the angular-momentum interpretation of electromagnetic fields, experimental schemes feasible in modern laboratories are suggested.
Over the past three decades or so, experiments of the type called Gedanken have become real. Recall the Schrödinger quote from Chapter 8: “… we never experiment with just one electron or atom or (small) molecule.” This is no longer true. We can do experiments involving single atoms or molecules and even on single photons, and thus it becomes possible to demonstrate that the “ridiculous consequences” alluded to by Schrödinger are, in fact, quite real. We have already discussed some examples of single-photon experiments in Chapter 6, and in Chapter 10 we shall discuss experiments performed with single atoms and single trapped ions. In the present chapter, we shall elaborate further on experimental tests of fundamentals of quantum mechanics involving a small number of photons. By fundamental tests we mean tests of quantum mechanics against the predictions of local realistic theories (i.e. hidden variable theories). Specifically, we discuss optical experiments demonstrating violations of Bell's inequalities, violations originally discussed by Bell in the context of two spin-one-half particles. Such violations, if observed experimentally, falsify local realistic hidden-variable theories. Locality refers to the notion, familiar in classical physics, that there cannot be a causal relationship between events with space-like separations. That is, the events cannot be connected by any signal moving at, or less than, the speed of light; i.e. the events are outside the light-cone. But in quantum mechanics, it appears that nonlocal effects, effects seemly violating the classical notion of locality in a certain restricted sense, are possible.